# jobshop.ppt - Introduction to Job Shop Scheduling Problem...

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Introduction to Job Shop Scheduling Problem Qianjun Xu Oct. 30, 2001

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Description of Job Shop Scheduling A finite set of n jobs Each job consists of a chain of operations A finite set of m machines Each machine can handle at most one operation at a time Each operation needs to be processed during an uninterrupted period of a given length on a given machine Purpose is to find a schedule, that is, an allocation of the operations to time intervals to machines, that has minimal length
Formal Definition of JSS Job set Machine set Operations Each operation has processing time On O define A, a binary relation represent a precedence between operations. If then v has to be performed before w. A induce the total ordering belonging to the same job; no precedence exist between operations of different jobs. } ... , , { 2 1 n j j j J } ... , , { 2 1 m m m m M } ,... , { 2 1 i im i i i o o o O } ,... , { 2 1 i im i i } ... , , { 2 1 n o o o O A w v ) , (

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Formal Definition of JSS cont. A schedule is a function that for each operation v defines a start time S(v). A schedule S is feasible if The length of a schedule S is The goal is to find an optimal schedule, a feasible schedule of minimum length., min(len(S)).
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